How to move a selected mesh in to another collection in editmode?
An object can be made of many connected or unconnected meshes. Creating a new mesh in edit mode will not make it a new object, but will be part of the Active Object

You need to separate those meshes into different objects before they can be part of different collections.

To separate parts of a mesh and turn them into a new independent objects (with their own unique name and pivot point), use the separate function (pressing P) and choose if you want to separate by selection, unconnected parts or materials.

Read: Why can&#39;t objects in Edit Mode have their own name?